Some vehicle power steering systems use an actuator coupled to the steering shaft to provide power assist in vehicle steering. It is often desirable in such systems to provide a return torque command to the actuator so as to help return the steering gear to a centered position and provide a stable steering feel to the vehicle operator. Such a return torque command is generated as a function of steering position as shown in the graph of FIG. 4, provided the steering position is known. Rotational position sensors having high resolution and other desirable characteristics may be coupled to the steering shaft to provide an output voltage varying in a substantially linear manner from a first voltage to a second voltage through a rollover angle comprising an entire 360 degree rotation or some sub-multiple thereof. But the steering shaft typically rotates through a plurality of such revolutions or sub-multiple angles, and therefore a plurality of repetitions of the rollover angle, as the rack is moved from one end to the other of its operational range. Thus, a sensor directly coupled to the steering shaft for maximum resolution in the output signal is similarly rotated through a plurality of repetitions of the output voltage range and produces a rollover transition at the end of each repetition when the voltage jumps from one extreme to the other. The output of a sensor so coupled does not by itself provide a unique absolute steering position; rather, it provides a set of steering positions separated by a rollover angle corresponding to the full output voltage range. It is thus necessary, in order to know the absolute rotational position, to compensate the sensor output signal for such rollover transitions. But an offset parameter must also generally be generated every time a new vehicle ignition cycle is initiated, since the sensor may have been rotated into a different range of its output when the ignition was off, with no rollover transition being sensed.
When operation of a vehicle with such a steering system is initiated, it is not known for certain whether the steering position is right or left of center; and provision of return torque in the wrong direction could create just the opposite effect from that desired. It is therefor desirable to determine the steering system's absolute rotational position with some degree of confidence before applying full return torque. In addition, once the absolute steering position is known, it is preferable to phase in the return torque in a gradual, controlled manner that is not objectionable to the vehicle operator.